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On a Functional Equation

Published online by Cambridge University Press:  21 January 2009

T. W. Chaundy  and
J. B. McLeod
J. B. McLeod
Affiliation:
Christ Church, Oxford, Wadham College, Oxford
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We have recently discussed in (1) the general solution of a certain functional equation arising in statistical thermodynamics, and we propose in this note to deal with another functional equation arising from the same source(2).

The problem is to obtain the most general function f(x) which, for all positive integral values of m, n, satifies the functional equation

where

where A is an arbitrary constant. It is the object of this note to prove that this is the only continuous solution.

Type
Research Article
Information
Edinburgh Mathematical Notes , Volume 43 , December 1960 , pp. 7 - 8
Copyright
Copyright © Edinburgh Mathematical Society 1960

References

REFERENCES

(1)Chaundy, T. W. and Mcleod, J. B., On a functional equation, Quart. J. of Math. (Oxford) (2), 9 (1958), 202–6.CrossRefGoogle Scholar
(2)Brown, W. B., American J. of Phys., (to appear.)Google Scholar